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प्रश्न
Four alternative answers for the following question is given. Choose the correct alternative
In a cyclic ▢ABCD, twice the measure of ∠A is thrice the measure of ∠C. Find the measure of ∠C?
विकल्प
36°
72°
90°
108°
उत्तर
ABCD is a cyclic quadrilateral.
2∠A = 3∠C .....(1) (Given)
Now,
∠A + ∠C = 180º ......(Opposite angles of a cyclic
quadrilateral are supplementary)
⇒`3/2` ∠C + ∠C = 180º [From (1)]
⇒ `5/2`∠C = 180º
⇒ ∠C = `(2 xx 180º)/5` = 72º
Thus, the measure of ∠C is 72º.
Hence, the correct answer is 72º.
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